Numerical solution of three-dimensional N-S equations and energy in the case of unsteady stagnation-point flow on a rotating vertical cylinder

Abstract

The three-dimensional unsteady problem of impulsive stagnation-point flow on a rotating vertical circular cylinder along with mixed convection heat transfer has been solved, numerically for the first time. This is because similarity solution techniques are not always possible to be accomplished. Initially, the fluid is considered to be at rest and with a uniform temperature T∞ and at t = 0 it starts flowing toward a vertical cylinder at the strength rate of k¯ and the cylinder surface's temperature rises to Tw, simultaneously. The cylinder possesses a rotational movement, with a constant angular velocity ω. The Navier-Stokes and energy equations in cylindrical coordinate system have been descritized and solved in a 2-D domain by using a SIMPLE based algorithm. The buoyancy effects are also included in the computations, so the problem is investigated as mixed convection heat transfer. Considering a sample case of incompressible flow with Re = 1,5,10,15,20 and Pr=0.7, the results of Nusselt number, wall shear-stress and dimensionless velocity and temperature have been obtained at different states of cylinder's wall temperature and for some selected values of Grashof numbers.